Problem 12
ACT Scores A random survey of 1000 students nationwide showed a mean ACT score of 21.4 . Ohio was not used. A survey of 500 randomly selected Ohio scores showed a mean of 20.8 . If the population standard deviation is \(3,\) can we conclude that Ohio is below the national average? Use \(\alpha=0.05 .\)
Problem 13
Instead of finding the mean of the differences between \(X_{1}\) and \(X_{2}\) by subtracting \(X_{1}-X_{2},\) you can find it by finding the means of \(X_{1}\) and \(X_{2}\) and then subtracting the means. Show that these two procedures will yield the same results.
Problem 13
For Exercises 7 through \(27,\) perform these steps. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Victims of Violence A random survey of 80 women who were victims of violence found that 24 were attacked by relatives. A random survey of 50 men found that 6 were attacked by relatives. At \(\alpha=0.10,\) can it be shown that the percentage of women who were attacked by relatives is greater than the percentage of men who were attacked by relatives?
Problem 14
For Exercises 9 through \(24,\) perform the following steps. Assume that all variables are normally distributed. a. State the hypotheses and identify the claim. b. Find the critical value. c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Carbohydrates in Candy The number of grams of carbohydrates contained in 1 -ounce servings of randomly selected chocolate and nonchocolate candy is shown. Is there sufficient evidence to conclude that there is a difference between the variation in carbohydrate content for chocolate and nonchocolate candy? Use \(\alpha=0.10 .\) $$ \begin{array}{llllllll}{\text { Chocolate }} & {29} & {25} & {17} & {36} & {41} & {25} & {32} & {29} \\ {} & {38} & {34} & {24} & {27} & {29} & {} & {} \\\ {\text { Nonchocolate }} & {41} & {41} & {37} & {29} & {30} & {38} & {39} & {10} \\ {} & {29} & {55} & {29} & {}\end{array} $$
Problem 14
Monthly Social Security Benefits The average monthly Social Security benefit for a specific year for retired workers was dollar 954.90 and for disabled workers was dollar 894.10 . Researchers used data from the Social Security records to test the claim that the difference in monthly benefits between the two groups was greater than dollar 30 . Based on the following information, can the researchers' claim be supported at the 0.05 level of significance? $$ \begin{array}{lcc}{} & {\text { Retired }} & {\text { Disabled }} \\ \hline \text { Sample size } & {60} & {60} \\ {\text { Mean benefit }} & {\$ 960.50} & {\$ 902.89} \\ {\text { Population standard deviation }} & {\$ 98} & {\$ 101}\end{array} $$
Problem 14
For Exercises 7 through \(27,\) perform these steps. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Hypertension It has been found that \(26 \%\) of men 20 years and older suffer from hypertension (high blood pressure) and \(31.5 \%\) of women are hypertensive. A random sample of 150 of women are hypertensive. from recent hospital records, and the following results were obtained. Can you conclude that a higher percentage of women have high blood pressure? Use \(\alpha=0.05 .\) Men 43 patients had high blood pressure Women 52 patients had high blood pressure
Problem 15
Self-Esteem Scores In a study of a group of women science majors who remained in their profession and a group who left their profession within a few months of graduation, the researchers collected the data shown here on a self-esteem questionnaire. At \(\alpha=0.05,\) can it be concluded that there is a difference in the self-esteem scores of the two groups? Use the \(P\) -value method. $$ \begin{array}{ll}{\text { Leavers }} & {\text { Stayers }} \\\ {\bar{X}_{1}=3.05} & {\bar{X}_{2}=2.96} \\ {\sigma_{1}=0.75} & {\sigma_{2}=0.75} \\ {n_{1}=103} & {n_{2}=225}\end{array} $$
Problem 15
Hospital Stays for Maternity Patients Health Care Knowledge Systems reported that an insured woman spends on average 2.3 days in the hospital for a routine childbirth, while an uninsured woman spends on average 1.9 days. Assume two random samples of 16 women each were used in both samples. The standard deviation of the first sample is equal to 0.6 day, and the standard deviation of the second sample is 0.3 day. At \(\alpha=0.01,\) test the claim that the means are equal. Find the \(99 \%\) confidence interval for the differences of the means. Use the \(P\) -value method.
Problem 15
For Exercises 7 through \(27,\) perform these steps. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Commuters A recent random survey of 100 individuals in Michigan found that 80 drove to work alone. A similar survey of 120 commuters in New York found that 62 drivers drove alone to work. Find the \(95 \%\) confidence interval for the difference in proportions.
Problem 16
Ages of Homes Whiting, Indiana, leads the "Top 100 Cities with the Oldest Houses" list with the average age of houses being 66.4 years. Farther down the list resides Franklin, Pennsylvania, with an average house age of 59.4 years. Researchers selected a random sample of 20 houses in each city and obtained the following statistics. At \(\alpha=0.05,\) can it be concluded that the houses in Whiting are older? Use the \(P\) -value method. $$ \begin{array}{ccc}{} & {\text { Whiting }} & {\text { Franklin }} \\ \hline \text { Mean age } & {62.1 \text { years }} & {55.6 \text { years }} \\\ {\text { Standard deviation }} & {5.4 \text { years }} & {3.9 \text { years }}\end{array} $$
